Learn How to Pronounce cosh, sinh, and Gradient Symbols Easily

[chrisych]

Can anyone tell me how to pronounce the following symbols?

cosh, sinh and the gradient (the up-side-down delta).

hyperbola cosine? hyperbola sine? gradient?

 

[Gib Z]

Full names would be Hyperbolic Cosine, Hyperbolic Sine, and the backward difference operator.

 

[HallsofIvy]

The pronuciations "cosh" and "sinch" are commonly used. (In my Freshman calculus class the instructor said "sinus hyperbolicus"!)

The gradient operator (not the "backward difference operator") is commonly pronounced "grad" or "del" (that's more general, for example $\nabla f$ is "grad f" or "del f" while $\nabla \cdot \vec{f}$ is "div f" or "del dot f" and $\nabla \times \vec{f}$ is "curl f" or "del cross f" . Technically, it's a "nabla". In order to get that symbol in the tex above, I used "\nabla".

 

[neutrino]

I was taught 'cosh' and 'shine'. (If you're wondering, hyperbolic tangent was 'than' )

 

[CompuChip]

"Sinus hyperbolicus" is what I call it too, but not in English

[...]$\nabla X \vec{f}$ is "curl f" or "del cross f" . Technically, it's a "nabla". In order to get that symbol in the tex above, I used "\nabla".

Now if only you have used "\times" to get the cross symbol ...

 

[K.J.Healey]

Nabla! Thats great. A hebrew word for a type of harp or so I wiki.

When I read words to myself "cosh" and "sinh"
I SAY "Cosine" and then THINK "hyperbolic";
same with the Sin(h). Its weird.
I never actually used them in a sentence when alone. If talking ot someone else I say hyperbolic sine.

 

[GoldPheonix]

...

"Sinus hyperbolicus" is what I call it too, but not in English

Are you from Romania?

 

[Gib Z]

The gradient operator (not the "backward difference operator") is commonly pronounced "grad" or "del" ...

Sorry Halls, I actually have no personal experience with this what so ever (although I have many times manually just applied $f(x)-f(x-1)$ ), so this was somewhat new to me.

However extremely coincidentally, in my thread "How Good Am I?" (which I am sad you don't participate in :( ), yip just introduced to us an operator like that in one of his questions, and also in "Klaus_Hoffman"'s thread about the n-th difference of a function, lurflurf posted a link on wikipedia about Newton Series. When you press his link, it re directs to the article for the Difference Operator (http://en.wikipedia.org/wiki/Difference_operator) and it was over there where I got the name "backward difference Operator" :( Perhaps it is called different things in different fields of mathematics? Or a less common name this is?

In mathematics, a difference operator maps a function, f(x), to another function, f(x + a) − f(x + b).

The forward difference operator

$$\Delta f(x)=f(x+1)-f(x)$$

occurs frequently in the calculus of finite differences, where it plays a role formally similar to that of the derivative, but used in discrete circumstances. Difference equations can often be solved with techniques very similar to those for solving differential equations. Analogously we can have the backward difference operator

$$\nabla f(x)=f(x)-f(x-1)$$

When restricted to polynomial functions f, the forward difference operator is a delta operator, i.e., a shift-equivariant linear operator on polynomials that reduces degree by 1.

 

[CompuChip]

Are you from Romania?

Are you?

Nope, I'm from the land of tulips and clogs - I mean, [/color] 't Hooft and van der Waals

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